This information relates to digital display systems.
A digital display is normally formed as an array of picture elements whose intensities can be individually controlled. Examples are digitally controlled raster-scanned CRTs and digital plotters. Early displays used only two values for the intensity of the picture elements, but more recent displays have allowed a greater range of intensities, either as a gray-scale monochrome display or as part of a color display.
The intensity with which each picture element is to be displayed is obtained by sampling the desired image. The crudest form of sampling simply assigns each picture element the intensity of the image at the centre point of the element. However it is well known that this approach leads to objectionable artifacts in the displayed image such as jagged edges, lines and Moire fringes in closely spaced lines. It is known that these effects can be suppressed by better sampling techniques which sample the image beyond the center points of the picture elements. When such a technique is used, when an edge passes between the center of two picture elements both elements are illuminated and their intensities depend on the distance from each of them to the edge. This approach yields smoother-looking edges and allows an apparent positioning to less than the spacing between picture-element center.
A digital system may retain a definition of the required image in one of two forms. First the image may be a pre-defined set of samples which have previously been obtained either from sampling the external scene (obtained e.g. as a TV image), or by synthetic composition of symbols (e.g. a character display). Alternatively, the image may be defined as a set of geometric figures (lines, circles, etc) which are to be converted to an image as and when required.
The correct generation of samples in systems of the first case is the subject of much published material, and if the image is of an external scene is generally implemented in image processing programs. In the specific case of synthetic generation of characters, samples of the desired character image are calculated to align with the sampling grid, and therefore avoid the worst of the visual defects. This technique is used in most character display devices. Improvements to this commonplace implementation were described in U.S. Pat. No. 4,158,200 to Seitz et al. This system used a pre-defined set of samples, which incorporated varying gray levels, in order to generate a smooth well shaped character on a display screen. The samples were stored in place of the conventional character ROM of such a character display system, but were precalculated to lie on the screen at a particular size, angle, and position relative to the raster scan of the display.
The transformation in size, angle, or position of an image represented by a pre-defined set of samples cannot easily be implemented owing to the fact that detail has been lost in the original sampling process. Because of this limitation systems which are required to provide such transformations use the alternative of defining the image as a set of geometrical figures. Geometric functions, such as ax+by=c represent lines at any required resolution and can be transformed without loss of detail before sampling. This approach yields much superior results.
A sampling method for use in these circumstances is described in "The aliasing problem in computer-generated shaded images" by F. C. Crow, Communications of the AGM, November 1977, pages 799 to 805. This method derives each sample value by two dimensional integration of the neighbourhood of the sample. The geometric function is first calculated at a finer resolution than the sampling grid, the resultant fine image passed through a two dimensioned weighted integration, and the result used as the value for the sample point corresponding to the center of the integration. The result of this process is that visible defects caused by sampling are substantially suppressed in the final image. Unfortunately the computation of the integration consumes significant power and therefore this method is not generally adopted by implementors.
A simpler procedure for displaying lines is described in "Filtering edges for gray-scale displays" by S. Gupta and R. F. Sproull in Computer Graphics, August 1981, pages 1 to 5. The intensity of a picture element near the line is determined from its perpendicular distance from the line. For each possible distance the appropriate intensity is precalculated using a two-dimensional integration and the results are loaded into a look-up table. This table is addressed by the perpendicular distance of the picture element from the line to obtain its intensity. The advantage of using the perpendicular distance is that the intensities may be calculated once only and then used whatever the angle of the line on the display. It is still however necessary to decide which elements to treat in this way. The article uses a modification of Bresenham's Algorithm. For a line of unit width--taking the distance between the center of neighbouring picture elements as the unit of distance--the picture elements which will be illuminated to display the line are chosen in threes. If the line lies in the first octant (that is, makes an angle with the horizontal in the range 0.degree. to 45.degree.) the line is displayed by illuminating three picture elements in each column. Starting from the three elements representing the line in one column the three elements representing it in the next column to the right are obtained by displacing the original three elements either horizontally to the right or diagonally up at 45.degree.. Which possibility is chosen is governed by which of the two possible positions for the center element of the three lies closest to the center of the line being represented.